Honors Algebra 2 B Semester Exam Review 2015–2016

Honors Algebra 2 B
Semester Exam Review
Honors Algebra 2 B
Semester Exam Review
2015–2016
© MCPS
Page 1
Honors Algebra 2 B
Semester Exam Review
Exam Formulas
P  x, y 
For the circle x 2  y 2  r 2 :
Circumference = 2 r
If  is an angle in standard position, whose terminal
ray passes through P  x, y  on the circle, then:

r
y
r
x
cos  
r
y
tan  
x
2
sin   cos 2   1
sin  
180 degrees   radians
If A and B are two events, then
P  A | B 
P  A and B 
P B
P  A or B   P  A  P  B   P  A and B 
P  A and B   P  A  P  B | A
© MCPS
Page 2
Honors Algebra 2 B
Semester Exam Review
The Standard Normal Distribution
34%
34%
13.5%
0.15%
13.5%
2.35%
2.35%
0.15%
Standard Deviations from the Mean
Mean
z -score 
© MCPS
data score  mean
standard deviation
Page 3
Honors Algebra 2 B
Semester Exam Review
Unit 2, Topic 3
1.
The graphs below are transformations of y 
a.
1
. Write the equation for each graph.
x
b.
2.
Graph the following.
a.
y  3
© MCPS
1
x 1
b.
y  2 
1
x 3
Page 4
Honors Algebra 2 B
3.
Write the least common multiple of the denominators in each equation, then solve the
equations. Check for extraneous solutions.
a.
4.
Semester Exam Review
7
5

x3 x2
Look at the graphs of f  x  
3x  6
x 1

 x  2  x  2 x  2
b.
1
1
and g  x   2 .
x
x
Complete the table below for each function.
Function f  x  
1
x
Function g  x  
1
x2
Even, odd, or neither
Domain
Range
End behavior as x  
End behavior as x  
© MCPS
Page 5
Honors Algebra 2 B
5.
6.
Semester Exam Review
A house with a total wall surface area of 4,500 square feet is to be painted. Each painter
can paint 300 square feet of surface in one hour.
a.
How long will it take one painter to paint the house?
b.
Complete the blank. The number of hours that it takes to paint the house varies
_____________ as the number of painters.
c.
Let n be the number of painters assigned to this job, and let H represent the total
number of hours it will take for the paint job to be complete. Use your answer to
part a) to write an equation relating H and n.
d.
How many hours will it take if 4 painters are assigned to this job?
Write an equation relating the variables in this situation. The number of hours, H, to
drive 200 miles varies inversely as the speed of the car, s, in miles per hour.
© MCPS
Page 6
Honors Algebra 2 B
7.
a.
Show that the functions f and g below are equivalent.
f  x  2 
8.
Semester Exam Review
1
x3
g  x 
2x  7
x3
b.
What are the equations of the asymptotes of the graphs?
a.
Show that the functions h and z are equivalent.
h  x  5 
b.
© MCPS
1
x4
z  x 
5 x  21
x4
What are the equations of the asymptotes of the graphs?
Page 7
Honors Algebra 2 B
9.
10.
Semester Exam Review
Brianna bakes cakes. The average cost, C, in dollars, to make x pound cakes in a day is
250  6x
.
given by the formula C 
x
a.
If Brianna bakes 10 pound cakes in one day, what was her average cost per pound
cake made?
b.
One day, Brianna’s average cost to make each pound cake was $11. Write and
solve an equation to determine how many pound cakes she made that day.
Brandi makes fruitcakes. She always gives 2 fruit cakes a day to charity. The average
500  8 x
, where x is the
cost per fruitcake sold, S, in dollars, is given by the formula S 
x2
number of fruitcakes made.
a.
One day, Brandi made 22 fruitcakes. What was the average cost per fruitcake
sold?
b.
On another day, the average cost per fruitcake sold was $18.75. Write and solve
an equation to determine how many fruitcakes she made.
© MCPS
Page 8
Honors Algebra 2 B
Semester Exam Review
Unit 3
11.
An angle  in standard position passes through a point P  x, y  in the coordinate plane.
Complete the table below.
Values of x and y
x is positive, y is positive
x is positive, y is negative
x is negative, y is positive
x is negative, y is negative
12.
Quadrant of the Angle 
Sign of cos 
In each part below, a circle centered at the origin is shown, with an angle  . For each
figure, determine sin  , cos  , and tan  , and the measure of the angle to the nearest tenth
of a degree.
a.
b.

P 2, 5

P  4,1

13.
Sign of sin 

sin   _____
sin   _____
cos   _____
cos   _____
tan   _____
tan   _____
  ______
  ______
An angle  is in quadrant 3 with sin   
© MCPS
5
. What is the value of cos  ?
13
Page 9
Honors Algebra 2 B
14.
Semester Exam Review
What statement is true about the Pythagorean identity sin 2 t  cos 2 t  1 ?
Select all that apply.
_____ Any real number can be used for t.
_____ Any degree-measured angle can be used for t.
_____ Any radian-measured angle can be used for t.
15.
Look at the unit circle below. A point rotates 80o counter-clockwise from point P to point R.
R
t
O
F
P 1, 0 
a.
What is the length, in units, of t? You may leave your answer in terms of  .
b.
Which segment has a length representing sin t ? ______
c.
Which segment has a length representing cos t ? ______
d.
Write the ratio of two segment lengths representing tan t . ______
e.
Name two angles who sine value is the same as sin 80o .______ and ______
f.
Name two angles whose cosine value is the same as cos t . _____ and _____
© MCPS
Page 10
Honors Algebra 2 B
16.
Semester Exam Review
The tables below represent values from a sine or cosine function. If each were graphed,
state the amplitude, period, and equation of the midline of the graph.
a.
0
50
x
y
1
40
2
30
Amplitude: ______
3
20
4
10
5
20
Period = _______
6
30
7
40
8
50
9
40
10
30
11
20
12
10
Equation of midline ________________
b.
0


18
8
10
4
2
x
y
Amplitude: ______
17.
3
8
10

2
18
5
8
10
Period = _______
3
4
2
7
8
10

18
9
8
10
5
4
2
11
8
10
3
2
18
Equation of midline ________________
Let f  x   cos x . The four graphs described below are transformation of function f.
Write the function equation for each.
a.
The graph of function g is the result of the graph of function f being dilated
vertically by a factor of three. g  x   ___________________
b.
The graph of function h is the result of the graph of function f being translated to
the left four units and up six units. h  x   ___________________
c.
The graph of function k is the result of the graph of function f being dilated
horizontally by a factor of 7. k  x   ___________________ .
d.
The graph of function p is the graph of function f being dilated horizontally and
1
vertically by a factor of . p  x   ___________________
2
© MCPS
Page 11
Honors Algebra 2 B
Semester Exam Review
At a local carnival, there is a pony ride. A person gets to ride a pony in a circle. There is a fence
near the circular path. Here is some information about the pony ride.
The circular path has a radius of 15 feet. The pony travels at a constant speed and completes one
counterclockwise rotation every 36 seconds. The distance from the fence to the center of the
circle is 20 feet. A view from above shows this information.
S
One counterclockwise
rotation every
36 seconds.
Pauline’s mom wants to take some pictures and needs to know how far Pauline is from the fence
at any point in time.
18.
Pauline’s mother starts timing  t  0 seconds  when she is at point S, 20 feet from the
fence. Determine the distance that Pauline is from the fence after she has rotated the
following number of degrees counterclockwise from point S. Round your answers to the
nearest tenth of a foot.
19.
a.
40o ________
d.
Show how you determined your answer to part a).
b.
117o ________
c.
230o _________
Determine how many feet Pauline is from the fence at the following times t. Round your
answers to the nearest tenth of a foot.
a.
1 second _______
d.
Show how you determined your answer to part c)
© MCPS
b.
24 seconds _______ c.
31 seconds _______
Page 12
Honors Algebra 2 B
Semester Exam Review
Continuation of item from previous page.
20.
Sketch a graph that represents the distance Pauline is from the fence on the time
interval  0,36 .
d
t
21.
What is the amplitude, period, and equation of the midline of the graph?
Amplitude: ______
Period: _______
Equation of midline: ________
22.
Write an equation, for the distance that the pony is from the fence as a
function of time.
© MCPS
Page 13
Honors Algebra 2 B
Semester Exam Review
Unit 4:
23.
As a science assignment, Kylie and Christine are asked to write a report on how the
distance from a light source affects how a person’s eyes view its intensity. They purchase
a light intensity meter and a flashlight. They move the meter away from the light and
measure the intensity at different distances. Here is some of their data.
Distance (meters)
1
2
3
4
5
a.
Light Intensity (Lux)
320
80
35.6
20
10
Kylie would like to present this model in the form of a table as their complete
report. Is this a good idea? Explain why or why not.
Christine does some research and finds that the intensity of light (I) varies
inversely as the square of the distance (d) from the light source. After doing some
320
calculations, she presents a model as the formula I  2 .
d
b.
Show that Christine’s formula gives the same results as Kylie’s table for t  2
and t  4 .
c.
What are the allowable values for d in Christine’s formula?
© MCPS
Page 14
Honors Algebra 2 B
Semester Exam Review
Continuation of item from the previous page.
Kylie thinks that a graph would be a good model. Here is her graph.
d.
Jake wants to know what distance would result in a light intensity of 1.6 lux.
Which model (table, formula, or graph) do you think would be the best model to
use in order to answer Jake? In your answer tell how you would use the model
you chose, and why you did not choose the other two models.
© MCPS
Page 15
Honors Algebra 2 B
24.
Semester Exam Review
Jackie is studying the following sequence of numbers.
1, 5, 14, 30
She believes that she has found two possible models for this sequence.
Recursive model:
f 1  1
f  n   f  n  1  n 2
Explicit model: f  n  
n  n  1 2n  1
6
Part of the modeling process involves doing computations to determine whether or not a
model accurately reproduces the situation. Determine if each of Jackie’s models are
appropriate.
© MCPS
Page 16
Honors Algebra 2 B
25.
Semester Exam Review
Name the two different function types that are added to produce each graph below.
a.
b.
26.
James wants to model the following data.
0
0
x
y
a.
b.
1
40
2
80
3
40
4
0
5
40
6
80
7
40
8
0
Which type of function would best model this data? Give a reason for your
answer.
Robert states that the equation y  40  40sin  90 o x  is a good model for this
data. Is Robert correct? If so, explain why. If not, modify his model to make it
correct.
© MCPS
Page 17
Honors Algebra 2 B
27.
Semester Exam Review
Yolanda makes a sketch in the coordinate plane made up of straight line segments. The
tables below show the x- and y-coordinates of the position of her pencil as a function of
time.
t
0
1
2
3
4
5
x
–4
–3
–1
0
3
4
t
0
1
2
3
4
5
y
3
3
0
–1
2
–2
Sketch Yolanda’s graph of on the coordinate grid below.
© MCPS
Page 18
Honors Algebra 2 B
Semester Exam Review
Unit 5
28.
A person flips a two-sided coin (heads or tails) and rolls a six-sided number cube
(numbers 1, 2, 3, 4, 5, 6). How many different outcomes are there?
29.
In the Venn Diagrams below, the events shown are
R: A person who likes to run and B: A person who likes to bike.
In each situation below, shade in the appropriate areas.
a.
People who like to ride and like to bike.
R
b.
B
People who like to ride or like to bike.
R
c.
B
People who do not like to ride.
R
d.
People who like to ride, but do not like to bike.
R
© MCPS
B
B
Page 19
Honors Algebra 2 B
30.
Semester Exam Review
One-hundred people (male and female) were asked which of two sports they preferred
(hockey or basketball). The results are shown in the two-way table below.
Male (M)
Female (F)
Total
Hockey (H)
14
6
20
Basketball (B)
56
24
80
Total
70
30
100
One person is selected at random from this group. Determine the following.
a.
The probability that the person likes basketball.
b.
The probability that the person is female.
c.
The probability that the person prefers hockey and is male.
d.
The probability that the person prefers basketball and is female.
e.
The probability that the person is female or prefers hockey.
f.
The probability that the person is male or prefers basketball.
g.
Given that the person selected is male, the probability that the person prefers
hockey.
h.
Given that the person selected prefers basketball, the probability that the person is
female.
i.
Are “person is a male” and “person prefers hockey” independent events? Use
what you know about conditional probabilities to justify your answer.
© MCPS
Page 20
Honors Algebra 2 B
31.
Semester Exam Review
The Venn Diagram below shows the percentages of people who eat fruits (F) and
vegetables (V) at least once a day.
18%
F
42%
V
8%
32%
A person is selected at random. Determine the following.
a.
The probability that the person eats fruits.
b.
The probability that the person does not eat vegetables.
c.
The probability that the person eats fruits and vegetables.
d.
The probability that the person eats fruits or vegetables.
e.
The probability, given that the person eats fruits, also eats vegetables.
f.
The probability, given that the person eats vegetables, also eats fruits.
g.
The probability, the person does not eat vegetables and also does not eat fruits.
32.
The probability that Jay gets to works overtime on any given day is 40%. What is the
probability that Jay will have to work overtime on three consecutive days?
33.
Polly is interested in the upcoming two games played by her team. She decides that her
team has a 0.7 probability of winning game one, and a 0.6 probability of winning game
two. Assuming that the results of the games are independent, what is the probability of
her team winning both games?
34.
A machine that randomly gives out jelly beans has 4 cherry, 2 chocolate, and 5 peach
jelly beans in it. Bob buys 3 jelly beans. What is the probability that all three are peach?
© MCPS
Page 21
Honors Algebra 2 B
Semester Exam Review
Unit 6
35.
36.
The life span of a certain insect is normally distributed has a mean life span of 14 days
and a standard deviation of 2 days.
a.
What percentage of the population has a life span between 12 and 16 days?
b.
What percentage of the population has a life span greater than 18 days?
c.
What percentage of the population has a life span between 14 and 20 days?
d.
What percentage of the population has a life span less than 12 days?
e.
A particular insect lived for 24 days. Did this insect live unusually long? Use
what you know about standard deviation to explain your answer.
The graph shows normal distribution A with mean of 15 and standard deviation 1.
To its right is normal distribution B.
A
B
Complete blanks below with greater than, less than, or equal to.
a.
The standard deviation of distribution B is _______________ the standard
deviation of distribution A.
b.
The mean of distribution B is _____________ the mean of distribution A.
© MCPS
Page 22
Honors Algebra 2 B
37.
Semester Exam Review
Which statement is true about normal distributions? Select all that apply.
_____ The graph has a vertical line of symmetry at the mean.
_____ There is one mode, which has the same value as the mean and median.
_____ Approximately 68% of the data lie within 1 standard deviation of the mean.
_____ A data score with a z-score of 3 is further from the mean than a data score with a
z-score of –2.
38.
The president of Small-Mart is awarding “Store of the Year” to one of two stores. He
will give the award to the store that did the best relative to the stores in their respective
cities.
Here is the information that the president has.
City
Mean Sales for
ALL stores in
this city
Los Angeles
Milwaukee
$22.6 million
$15.1 million
Standard
deviation in
sales for all
stores in this
city
$2.2 million
$1.4 million
Store with the Sales of this
highest sales in store
this city
Goldie’s
Ahmed’s
$25.9 million
$17.9 million
Which store should receive the award? Justify your answer.
39.
The president of Small-Mart is also going to fire the manager of the store that has
performed the worst during the past year relative to the other stores in two other cities.
Here is the information that the president has.
City
Mean Sales for
ALL stores in
this city
New York
Seattle
$52.9 million
$30.2 million
Standard
deviation in
sales for all
stores in this
city
$6.3 million
$4.0 million
Store with the Sales of this
highest sales in store
this city
Jose’s
Jamal’s
$31.7 million
$14.4 million
Which store will have its manager fired? Justify your answer.
© MCPS
Page 23
Honors Algebra 2 B
40.
Semester Exam Review
The scores on a test taken by seniors are normally distributed with a mean of 27 and a
standard deviation of 2.
a.
Bob’s score was better than 84% of all scores. What was his score?
b.
Sally’s score was better than 2.5% of all scores. What was her score?
© MCPS
Page 24